Moore’s Law Moores law was a statement made in 1965 byGordon Moore, one of the founders of Intel. Moore noted that the number of transistorsthat could be squeezed on to a silicon chip wasdoubling every year. Over time, this has beenrevised to doubling every 18 months.This has held true …….. So far
Problems At current rate transistors will be as small as an atom. If scale becomes too small, Electrons tunnel through micro-thin barriers between wires corrupting signals.
Quantum Computing TimelineThe story of quantum computation started as early as1982, when the physicist Richard Feynmanconsidered simulation of quantum-mechanical objectsby other quantum systems1985 when David Deutsch of the University of Oxfordpublished a crucial theoretical paper in which hedescribed a universal quantum computer.In 1994 when Peter Shor from AT&Ts BellLaboratories in New Jersey devised the first quantumalgorithm.
Nobody understands Quantum Mechanics“We always have had a great deal of difficultyin understanding the world view thatquantum mechanics represents ”- Richard Feynman ("Simulating physics with computers" ,1982)
Representation of Data - Qubits A bit of data is represented by a single atom that is in one of two states denoted by |0> and |1>. A single bit of this form is known as a qubit A physical implementation of a qubit could use the two energy levels of an atom. An excited state representing |1> and a ground state representing |0>. Light pulse of frequency λ for Excited time interval t State NucleusGround State Electron State |0> State |1>
Properties Of Quantum Mechanics Quantum Superposition Quantum Entanglement
Representation of Data - SuperpositionA single qubit can be forced into a superposition of the two statesdenoted by the addition of the state vectors: ψ |ψ> = α 1 |0> + α 2 |1> αWhere α 1 and α 2 are complex numbers and |α 1| 2 + | α 2 | 2 = 1 A qubit in superposition is in both of the states |1> and |0> at the same time
Relationships among data - Entanglement Entanglement is the ability of quantum systems to exhibitcorrelations between states within a superposition. Imagine two qubits, each in the state |0> + |1> (a superpositionof the 0 and 1.) We can entangle the two qubits such that themeasurement of one qubit is always correlated to themeasurement of the other qubit.
Classical computation vs. Quantum ComputationClassical Computation Quantum Computation Data unit: bit Data unit: qubit = ‘1’ = ‘0’ =|1〉 =|0〉 Valid states: Valid states: x = ‘0’ or ‘1’ |ψ〉 = c1|0〉 + c2|1〉 x=0 x=1 |ψ〉 = |0〉 |ψ〉 = |1〉 |ψ〉 = (|0〉 + |1〉)/√2 0 0 1 1
Classical computation vs. Quantum ComputationClassical Computation Quantum ComputationMeasurement: deterministic Measurement: stochasticState Result of measurement State Result of measurementx = ‘0’ ‘0’ |ψ〉 = |0〉 ‘0’x = ‘1’ ‘1’ |ψ〉 = |1〉 ‘1’ |ψ〉 = |0〉 + |1〉 ‘0’ 50% √2 ‘1’ 50%
Quantum Algorithm:Shor’s Algorithm Shors algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, named after Peter Shor. The algorithm is significant because it implies that RSA, a popular public-key cryptography method, might be easily broken, given a sufficiently large quantum computer Like many quantum computer algorithms, Shors algorithm is probabilistic
Quantum Algorithm:Shor’s Algorithm Shors algorithm consists of two parts: A reduction, which can be done on a classical computer, of the factoring problem to the problem of order-finding. f(x) = axmod(N) A quantum algorithm to solve the order-finding problem The algorithm is dependant on Modular Arithmetic Quantum Parallelism Quantum Fourier Transform
Quantum Algorithm: Shor’s Algorithm In 2001, Shors algorithm was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits with a classical computer# bits 1024 2048 4096factoring in 2006 105 years 5x1015 years 3x1029 yearsfactoring in 2024 38 years 1012 years 7x1025 yearsfactoring in 2042 3 days 3x108 years 2x1022 years with potential quantum computer# bits 1024 2048 4096# qubits 5124 10244 20484# gates 3x109 2X1011 X1012factoring time 4.5 min 36 min 4.8 hours
Quantum computing incomputational complexity theory The class of problems that can be efficiently solved by quantum computers is called BQP, for "bounded error, quantum, polynomial time".
Practical Implementations Ion Traps Nuclear magnetic resonance (NMR) Optical photon computer Solid-state